Intersection Cohomology of S1 Symplectic Quotients and Small Resolutions

نویسنده

  • E. LERMAN
چکیده

We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the S equivariant cohomology of the original symplectic manifold and the fixed point data. The key idea is the construction of a small resolution of the symplectic quotient.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Intersection Cohomology of Singular Symplectic Quotients

We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That i...

متن کامل

Gromov–Witten invariants of symplectic quotients and adiabatic limits

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions to the symplectic vortex equations. Our main theorem asserts that the genus zero invariants of Hamiltonian group actions defined by these equations are related to the genus zero Gromov–Witten invariants of the symplectic quotient (in the monotone case) via a natural ring homomorphism from the equivariant ...

متن کامل

Quasimap Floer Cohomology for Varying Symplectic Quotients

We show that quasimap Floer cohomology for varying symplectic quotients resolves several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact Hamiltonian torus action containing an open subset of non-displaceable orbits and a codimension four singular set, partly answering a question of McDuff, and (ii) determine displaceability for most of the moment ...

متن کامل

The Cohomology Rings of Abelian Symplectic Quotients

Let M be a symplectic manifold, equipped with a Hamiltonian action of a torus T . We give an explicit formula for the rational cohomology ring of the symplectic quotient M//T in terms of the cohomology ring of M and fixed point data. Under some restrictions, our formulas apply to integral cohomology. In certain cases these methods enable us to show that the cohomology of the reduced space is to...

متن کامل

Abelianization for hyperkähler quotients

We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohom...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998